Josephus wrote:

"I have also taken a great deal of pains to obtain the learning of the Greeks, and understand the elements of the Greek language, although I have so long accustomed myself to speak our own tongue, that I cannot pronounce Greek with sufficient exactness; for our nation does not encourage those that learn the languages of many nations, and so adorn their discourses with the smoothness of their periods; because they look upon this sort of accomplishment as common, not only to all sorts of free-men, but to as many of the servants as please to learn them. But they give him the testimony of being a wise man who is fully acquainted with our laws, and is able to interpret their meaning; on which account, as there have been many who have done their endeavors with great patience to obtain this learning, there have yet hardly been so many as two or three that have succeeded therein, who were immediately well rewarded for their pains." —Antiquities of Judeans XX, XI.

Josephus' testimony on "Greek wasn't spoken in first century Israel" and "the extreme rarity in terms of a Jew knowing Greek" is also supported by Aramaic New Testament known as Aramaic Peshitta. 

Although Greek NT and the translations of Greek NT contradicts the testimony of Josephus by saying that there were Greeks who communicated with Jesus and Apostle Paul, still Aramaic NT supports the testimony of Josephus by saying that they were either Aramaean(s) or Pagan(s).

Below are some examples.

1. Mark 7:26 (NIV Translation) - "The woman was a Greek, born in Syrian Phoenicia. She begged Jesus to drive the demon out of her daughter." 

But in Mark 7:26 (Book "The Original Aramaic New Testament in Plain English", Page. 68) - "But she was a pagan woman from Phoenicia of Syria, and she was begging him to cast out the demon from her daughter."

2. Acts 20:21 (NIV) - "I have declared to both Jews and Greeks that they must turn to God in repentance and have faith in our Lord Jesus."

Acts 20:21 (Book "The Original Aramaic New Testament in Plain English", Page. 206) - "While I was testifying to the Jews and to the Aramaeans about returning to God and the faith in Our Lord Yeshua The Messiah."

3. Acts 19:17 (KJV) - "And this was known to all the Jews and Greeks also dwelling at Ephesus; and fear fell on them all, and the name of the Lord Jesus was magnified."

Acts 19:17 (Book "The Original Aramaic New Testament in Plain English", Page. 204) - "And this became known to all the Jews and Aramaeans dwelling in Ephesaus and great fear fell upon all of them, and the name of Our Lord Yeshua The Messiah was exalted."

Judean Wars (Book 1, Preface, Paragraph 1): "I have proposed to myself, for the sake of such as live under the government of the Romans, to translate those books into the Greek tongue, which I formerly composed in the language of our country, and sent to the Upper Barbarians. Joseph, the son of Matthias, by birth a Hebrew, a priest also, and one who at first fought against the Romans myself, and was forced to be present at what was done afterwards, [am the author of this work]."

In first century AD, Josephus points out that Aramaic was a widespread language and understood accurately among Aramaic speakers.

Josephus points out that Parthians, Babylonians, the remotest Arabians, and those of his nation beyond Euphrates with the Adiabeni knew accurately about Judean Wars by his means (mentioned below) and why he translated his work from the language of his country into Greek for Greeks and Romans.

Judean Wars Book 1 Preface, Paragraph 2 - "I thought it therefore an absurd thing to see the truth falsified in affairs of such great consequence, and to take no notice of it; but to suffer those Greeks and Romans that were not in the wars to be ignorant of these things, and to read either flatteries or fictions, while the Parthians, and the Babylonians, and the remotest Arabians, and those of our nation beyond Euphrates, with the Adiabeni, by my means, knew accurately both whence the war begun, what miseries it brought upon us, and after what manner it ended."

In Acts 1:19, Field of Blood was known to all the inhabitants of Jerusalem in their own language as Akeldama which is the transliteration of Aramaic words "Haqal Dama." 

According to Dead Sea Scrolls archaeologist, Yigael Yadin, Aramaic was the language of Hebrews in first century Israel and early second century until False Messiah Simon Bar Kokhba tried to revive Hebrew and make it as the official language of Hebrews during Bar Kokhba revolt (132-135 AD). 

Yigael Yadin noticed the shift from Aramaic to Hebrew during the time of Bar Kokhba revolt. In Book "Bar Kokhba: The rediscovery of the legendary hero of the last Jewish Revolt Against Imperial Rome" Yigael Yadin notes, "It is interesting that the earlier documents are written in Aramaic while the later ones are in Hebrew. Possibly the change was made by a special decree of Bar-Kokhba who wanted to restore Hebrew as the official language of the state"(page 181). 

In Book "A Roadmap to the Heavens: An Anthropological Study of Hegemony among Priests, Sages, and Laymen (Judaism and Jewish Life)" by Sigalit Ben-Zion (Page 155), Yadin remarked: "it seems that this change came as a result of the order that was given by Bar Kokhba, who wanted to revive the Hebrew language and make it the official language of the state." 

According to Book "Naming the Witch: Magic, Ideology, and Stereotype in the Ancient World" written by Kimberly B. Stratton (p. 232), Yadin suggests that Bar Kokhba was trying to revive Hebrew by decree as part of his messianic ideology.

Check the below links for more details.

https://right.orain.org/wiki/Language_of_Jesus_Christ

https://right.orain.org/wiki/New_Testament

This video about Aramaic New Testament is also recommended.

https://archive.org/details/NTAramaic